ROUNDING OFF NUMBERS.
Numbers can be approximated (or rounded) to make them easier to work with. A number can be approximated by rounding. Approximation or rounding creates a new number that is similar but not exactly equal to the original number.
Rounding numbers to the nearest 10,100,1000.
But before rounding a number we need to know the position of each digit in a number or the place value of each digit in a number.
The table below represent the position of each digit in a number to the left of a decimal point which is shown at the right end column box.
| Ten millions | Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones | Decimal point |
The table below represent the position of each digit in a number to the right of a decimal point which is shown at the left end column box.
| Decimal point | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths | Millionths | Ten millionths |
For example, a number like 6478.7 it has the following place value for its digits.
| 6 | 4 | 7 | 8 | . | 7 |
| Thousands | Hundreds | Tens | Ones | Decimal point | Tenths |
Hence in rounding a number you look at the number one place to the right of the level that you are rounding to and see whether it is closer to 0 or 10.
This means that if you’ve been asked to round to the nearest 10, you look at the ones. If you are rounding to three decimal places, you look at the ten thousandths (the fourth number to the right of the decimal point) and so on. If that number is 5 or over, you round up to the next number, and if it is 4 or under, the number remains the same.
For example a number 6478.7 could be rounded to:
-To the nearest whole number (=6479.0)
Explanation.
In this question we are rounding 6478.7 to the whole number (ones) place value which has number 8 and the next number to the right is 7 which is above five, hence we round up 8 to 9 and hence obtain a new number 6479.0
-To the nearest ten (=6480.0)
Explanation.
In this question we are rounding 6478.7 to the tens place value which has number 7 and the next number to the right is 8 which is above five, hence we round up 7 to 8 and hence obtain a new number 6480.0
-To the nearest hundred (=6500.0)
Explanation.
In this question we are rounding 6478.7 to the hundreds place value which has number 4 and the next number to the right is 7 which is above five, hence we round up 4 to 5 and hence obtain a new number 6500.0
-To the nearest thousand (=6000.0)
Explanation.
In this question we are rounding 6478.7 to the thousands place value which has number 6 and the next number to the right is 4 which is below five, hence the 6 remain the same and hence obtain a new number 6000.0
Try this
At its closest, Jupiter is about 390682810 miles from Earth. Write this distance to the nearest million miles.
APPROXIMATIONS OR ROUNDING OF DECIMAL NUMBERS.
For decimal numbers you can round a decimal number to different numbers of decimal places.
For example a number like 9.7362 could be rounded to:
-To one decimal place (=9.7000)
Explanation.
In this question we are rounding 9.7362 to one decimal place which has number 7 and the next number to the right is 3 which is below five, hence the 7 remains and we obtain a new number 9.7000
-To two decimal place (=9.7400)
Explanation.
In this question we are rounding 9.7362 to two decimal places which has number 3 and the next number to the right is 6 which is above five, hence we round the 3 to 4 and we obtain a new number 9.7400.
-To three decimal place (=9.7360)
Explanation.
In this question we are rounding 9.7362 to three decimal places which has number 6 and the next number to the right is 2 which is below five, hence the 6 remains and we obtain a new number 9.7360
Try this
The density of Hydrogen gas is 0.0899kg/m^3. Round this density to two decimal place.
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